Einstein did not plagiarize Poincaré - by Olivier Darrigol

    It is commonly believed that relativity theory was the creation of one man only, Albert Einstein in most cases, and Henri Poincaré in a few cases.

 In reality, relativity theory was the result of a collective effort in which a number of physicists and mathematicians participated, including Hendrik Lorentz, Henri Poincaré, Albert Einstein, and Hermann Minkowski.

     At the turn of the nineteenth and twentieth century, most physicists that optical and electromagnetic waves required a subtle medium, the ether, for their propagation; just as sound is propagated through the air. And they expected the motion of the earth through the ether to slightly affect the result of optical or electromagnetic experiments. In an attempt to explain the experimental failure to detect such effects, Lorentz introduced transformations of space, time, and field coordinates that left the fundamental field equations approximately invariant. In his view the transformed coordinates were purely formal: they were a convenient subterfuge to ease the theoretical analysis of moving optical or electromagnetic devices. And the formal invariance did not completely exclude the possibility that more refined experiments would someday detect the motion of the earth through the ether.

     In contrast, Poincaré believed that the ether was too immaterial a thing for its "wind" to have any effect on optical or electromagnetic experiments. This is the principle of relativity, as he first formulated in the last years of the nineteenth century. In other words, the outcome of any physical experiment should not be affected by a global, uniform translation of the experimental setup. In 1900, Poincaré realized that at least in a first approximation Lorentz's transformed space, time, and field coordinates were the coordinates measured by terrestrial observers moving through the ether, if only the measurements were done under natural conventions. In particular, Lorentz's "local time" was the time measured by moving observers who synchronized their clocks by optical means and ignored their motion with respect to the ether. Consequently, the formal invariance of the fundamental equations directly translated into the concrete invariance of phenomena ruled by these equations. 

    When, in 1904, Lorentz improved his transformations to get an almost complete invariance of the fundamental equations, Poincaré soon corrected them to get perfect invariance. Again, he associated this formal symmetry with the invariance of phenomena in any inertial frame of reference. Yet he did not completely abandon the ether. In his view there still was a "true time" measured by observers bound to the ether; and the time measured by moving observers was only an "apparent time." Of course, this distinction could only be a conventional one, since the principle of relativity forbade any experimental determination of the ether frame. Poincaré nonetheless maintained it in order to avoid reforming our ancestral, Newtonian concept of time.

    Poincaré published a summary of his results in the June 5th, 1905, issue of the Comptes rendus. On June 30th of the same year the Annalen der Physik received Albert Einstein's  famous memoir "On the electrodynamics of moving bodies." From the start Einstein assumed the principle of relativity and the light principle according to which the velocity in a given inertial frame is a constant. He redefined the concepts of space and time accordingly; he derived the Lorentz transformations; he proved the invariance of the Maxwell-Lorentz equations through them. His theory shared the same group of transformations as Poincaré's, and the experimental predictions were exactly the same  But it differed from Poincaré's in three important ways: It did without the ether; It placed the space and time measured in different inertial systems all on the same footing; and it divorced the "kinematics" (the relations between space and time measurements in various frames) from the field dynamics. Minkowski further increased the contrast between the two theories by defining a 4-dimensional spacetime structure through the Lorentz group (in the spirit of Felix Klein's Erlangen program, according to which a geometry is defined through the group of transformations).

    Having read Science and hypothesis, Einstein certainly knew about Poincaré's relativity principle and about his general criticism of the concepts of space and time. He was plausibly aware of Poincaré's interpretation of Lorentz's local time (1900), and also of the Lorentz transformations in the form of 1904. He is not likely to have seen Poincaré's article in the Compte rendus before writing his own. Whatever inspiration he may have found in his ample readings, his approach differed from Lorentz's and Poincaré's at the profound level of concept formation.

    From the previous, highly simplified sketch of the genesis of relativity theory, it should be clear that Lorentz, Poincaré, Einstein, and Minkowski all contributed to it. Any judgment on the relative importance of their contributions depends on a subjective decision about what matters most in relativity theory. If the important thing is Lorentz's transformations, then give credit to Lorentz since he had them almost exactly. If the relativity principle and its expression through the Lorentz group are most essential, then Poincaré's name should stand out. If the redefinition of the basic concepts of space and time is given precedence, then hail to Einstein and Minkowski. Traditionally, the redefinition of space and time is regarded as part and parcel of relativity theory. This may be why Einstein is often regarded as the single father of relativity theory as we now understand it.